Hydroxypropyl xanthan gum(HXG) was prepared from xanthan gum(XG) and propylene oxide under alkaline condition. Rheological and drag reduction properties of different concentrations of aqueous HXG and XG solution were ...Hydroxypropyl xanthan gum(HXG) was prepared from xanthan gum(XG) and propylene oxide under alkaline condition. Rheological and drag reduction properties of different concentrations of aqueous HXG and XG solution were studied. The micro-structure network of HXG and XG solutions was investigated by Cryo-FESEM. The results showed that HXG and XG solutions could exhibit shear thinning property. The apparent viscosity of6 g·L-1HXG solution was 1.25 times more than that of 6 g·L-1XG solution. The storage modulus G′ and the loss modulus G″ of HXG solutions were greater than those of XG solutions, and thixotropic and viscoelastic properties were more significant in HXG solutions. The HXG and XG solutions reduced the pressure drop of straight pipe, and the maximum drag reduction of 1 g·L-1HXG and XG in smooth tube reached 72.8% and 68.1%, respectively. Drag reduction rate was increased as the concentration increased. The HXG solution may become a new polymeric drag reducer.展开更多
Let P（t, n） and C（t, n） denote the minimum diameter of a connected graph obtained from a single path and a circle of order n plus t extra edges, respectively, and f（t, k） the maximum diameter of a connected grap...Let P（t, n） and C（t, n） denote the minimum diameter of a connected graph obtained from a single path and a circle of order n plus t extra edges, respectively, and f（t, k） the maximum diameter of a connected graph obtained by deleting t edges from a graph with diameter k. This paper shows that for any integers t ≥4 and n ≥ 5, P（4, n） ≤n-8/t＋1＋ 3, C（t,n）≤n-8/t＋1＋3 if t is odd and C（t,n） ≤n-7/t＋2 ＋3 if t is even; [n-1/5] ≤P（4,n） ≤ [n＋3/5] [n/4]-1≤C（3,n）≤[n/4]; and f（t, k）≥ （t ＋ 1）k - 2t ＋ 4 if k≥3 and is Odd, which improves some known results.展开更多
基金Supported by the National High Technology Research and Development Program of China(2013AA064801)
文摘Hydroxypropyl xanthan gum(HXG) was prepared from xanthan gum(XG) and propylene oxide under alkaline condition. Rheological and drag reduction properties of different concentrations of aqueous HXG and XG solution were studied. The micro-structure network of HXG and XG solutions was investigated by Cryo-FESEM. The results showed that HXG and XG solutions could exhibit shear thinning property. The apparent viscosity of6 g·L-1HXG solution was 1.25 times more than that of 6 g·L-1XG solution. The storage modulus G′ and the loss modulus G″ of HXG solutions were greater than those of XG solutions, and thixotropic and viscoelastic properties were more significant in HXG solutions. The HXG and XG solutions reduced the pressure drop of straight pipe, and the maximum drag reduction of 1 g·L-1HXG and XG in smooth tube reached 72.8% and 68.1%, respectively. Drag reduction rate was increased as the concentration increased. The HXG solution may become a new polymeric drag reducer.
基金the National Natural Science Foundation of China (10271114)
文摘Let P（t, n） and C（t, n） denote the minimum diameter of a connected graph obtained from a single path and a circle of order n plus t extra edges, respectively, and f（t, k） the maximum diameter of a connected graph obtained by deleting t edges from a graph with diameter k. This paper shows that for any integers t ≥4 and n ≥ 5, P（4, n） ≤n-8/t＋1＋ 3, C（t,n）≤n-8/t＋1＋3 if t is odd and C（t,n） ≤n-7/t＋2 ＋3 if t is even; [n-1/5] ≤P（4,n） ≤ [n＋3/5] [n/4]-1≤C（3,n）≤[n/4]; and f（t, k）≥ （t ＋ 1）k - 2t ＋ 4 if k≥3 and is Odd, which improves some known results.
